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Math Help - \int

  1. #1
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    \int

    Hello!
    Please, any good soul to help me with:
    \intx^2sin2xdx???
    The result is :
    \frac{1}{4}(1-2x^2)cos2x+\frac{1}{2}xsin2x+C

    Many thanks!!!
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  2. #2
    MHF Contributor

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    Re: \int

    Quote Originally Posted by marijakopljar View Post
    Hello!
    Please, any good soul to help me with:
    \int x^2sin2xdx???
    You left out the space between 'int' and 'x^2'. I added it.

    Use "integration by parts": \int u dv= uv- \int v du with u= x^2, dv= sin(2x)dx so that du= 2xdx, v= -\frac{1}{2}cos(2x). Doing that, you will still have an integral involving xcos(2x). So use integration by parts again, this time letting u= x, dv= cos(2x)dx.

    Generally speaking, any time you have an integral of x^n f(x)dx, you can consider repeated integration by parts, repeatedly taking the power of x as "u" so that when you differentiate to get du, you have one less power of x. Repeat until you have reduced the power of x to 0.


    The result is :
    \frac{1}{4}(1-2x^2)cos2x+\frac{1}{2}xsin2x+C

    Many thanks!!!
    Last edited by HallsofIvy; January 17th 2013 at 09:45 AM.
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